Computer circuit

ABSTRACT

A computer circuit for generating signals related to the ballistics of a plurality of projectile or ammunition types, the signals including time of flight, superelevation, and ballistics drift signals. The computer includes a plurality of parallel channels, including a first adjustable multiplier circuit, which operates on the range information by a selected ballistics normalizing transfer function to generate an individual normalized range signal for a selected individual one of the plurality of projectile or ammunition types, a function generator coupled to receive and operate on the normalized range signals with a nonlinear transfer function common to the ballistics of all of the projectile type for generating an exponential function signal related to the selected projectiles, and a second adjustable multiplier circuit coupled to the function generator for multiplying the function signal by a selected individual unnormalizing transfer function for the selected projectile type generating signals related to the ballistics of the projectile, such as superelevation and time of flight.

221 Filed June 24, 1968 [45] Patented July 6, 1971 [73] Assignee Hughes Aircraft Company Culver City, chm.

[54] COMPUTER CIRCUIT Ritchie et a1. The Design Of Biased Diode Function Generators" ELECTRONIC ENGINEERING June 1959. p. 347/351.

Galli: Nonideal Diodes And Practical Function Generators" CONTROL ENGINEERING Feb. 1960 p. 107/109 Primary ExaminerMalcolm A. Morrison Assistant Examiner- Felix D. Gruber 27 4 Drawing Figs Attorneys.lam es K. Haskell and Robert Thompson [52] U.S. Cl 2 35/6l.5 E,

[235/193, 23511917307030 [51] Int. Cl 606g 7/80,

606g 7/26 ABSTRACT: A computer circuit for generating signals related [50] Field of Search 235/61.5 E, to the ballistics f a plurality f projectile or ammunition 197; 343/10, 12, l6;33/49, 62; 89/l.5 E, 135,41, 41.6,41.61,41.62,4l.7,4l.7R,4l.7 L;244/3.l,

types, the signals including time of flight, superelevation, and ballistics drift signals. The computer includes a plurality of OR 3,591,772 SEARC ROOM 5 3 M v fiat .1" [72] Inventors William E.McAdam,,Ir. 3,373,263 3/1968 Cooper etal. 235/61.5 Thousand Oaks; FOREIGN PATENTS 2: cmerbmk' Angels 476,831 12/1937 Great Britain 235/6l.5 21 AppLNo, 739,420 OTHER REFERENCES 315 parallel channels, including a first adjustable multiplier circuit, which 0 erates on the range information by a selected [56] Reerences cued ballistics norr ilalizing transfer function to generate an in- UNXTED STATES PATENTS dividual normalized range signal for a selected individual one 3,296,428 1/1967 Nathan... 235/197 of the plurality of projectile or ammunition types, a function 3,506,810 4/1970 Katell 235/197 X generator coupled to receive and operate on the normalized 2,407,325 9/ 1946 Parkinson. 235/61 5 range signals with a nonlinear transfer function common to 2,833,470 5/1968 Welty 235/6l.5 the ballistics of all of the projectile type for generating an ex- 2,933,980 4/1960 Moore et a1. 89/1 ponential function signal related to the selected projectiles, 2,946,260 7/1960 Gray 89/1 .5 and a second adjustable multiplier circuit coupled to the func- 2,947,474 8/1960 Vance 235/61 5 tion generator for multiplying the function signal by a selected 3,048,087 8/1962 Campbell 89/41 individual unnormalizing transfer function for the selected 3,309,963 3/1967 Salomonsson.... 89/41 projectile type generating signals related to the ballistics of the 3,339,457 9/1967 Pun 89/41 projectile, such as superelevation and time of flight.

Z I VIVCT/O/i/ e 2;, j wwraz r 25/; ;z;.

2a 2 AA/i: Z/ 24 (W i p ,6 Z 1 .9 I ,rua ar/av Q a e-47016 5 o COMPUTER CIRCUIT This invention relates generally to ballistics computers, and relates more particularly to a ballistics computer for generating signals which are related to the ballistics of a plurality of projectiles or ammunitions.

Range information has heretofore been fed to a computer circuit which would produce output signals related to the ballistics of a projectile when the physical characteristics such as its velocity, ambient atmospheric condition, gravitational conditions, the shape, the mass, and the spin were known or assumed. Generally, these signals were generated by function generators which were specifically mechanized for each specific projectile. For example, function generators have been mechanized using electromechanical range followup servos to position the armatures of padded range function potentiometers. Since other projectiles could have other ballistics characteristics as a result of different velocities, masses, shapes, and so forth, it became necessary to remechanize the function generator so that the generated output signals were related to the ballistics of the new projectile.

SUMMARY OF THE INVENTION Accordingly, it is an object of this invention to provide improvements in a device which is operable to generate signals related to the ballistics of projectiles.

Another object of this invention is to provide an adjustable ballistic computer circuit which is operable to produce ballistics functions related to the, ballistics of a plurality of projectile types.

Still another object is to provide improvements in a ballistics computer having the advantages that: a single nonlinear function generator can be utilized for the ballistics of a plurality of projectile types; variations in nonstandard ballistics and environmental conditions including air density as a result of atmospheric pressure and temperature variation, variations in the drag coefficient as a result of changes in the mach number due to changes in air temperature, changes in muzzle velocity as a result of tube wear and propellant temperature, and changes in crosswind and range wind coefiicients as a result of any of the above can be compensated for outside of the function generator; and that lends itself to solidstate implementation, is simplified relative to other known devices, and has a small size.

Other objectives of this invention can be attained with a computer circuit having a plurality of parallel output channels wherein each channel is operable to receive range information. The range information R for several of the channels is fed through an adjustable ballistics term multiplier which normalizes the range information R with a specific range normalizing transfer function or term R derived from standard and nonstandard ballistic and environmental conditions for the selected projectile type. Thereafter, the normalized range information R/R is fed in parallel on each of the plurality of channels to a function generator which operates on the normalized range signal in accordance with a predetermined transfer function, which itself is normalized, and therefore is common to a multiplicity of projectile types. The output of each individual function generator is then fed to another individual adjustable ballistics term multiplier which operates on the received function signal with a specific unnormalizing transfer function to produce an output signal on each channel related to the selected projectile. The resulting output signals from these last-mentioned ballistics term multipliers include time of flight information I, and super elevation information 6,, related to the ballistics of the selected projectile at the particular range R. By selectively switching the two multipliers, the ballistics terms are changed to those associated with another selected projectile type.

Other objects, features and advantages of this invention will become apparent upon reading the' following detailed description and referring to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram illustrating an embodiment of the computer having a first ballistics term multiplier and two parallel channels each having a ballistics function generator and a second ballistics term multiplier for producing superelevation and time of flight signals;

FIG. 2 is a schematic diagram illustrating the details of any one of the ballistics term multipliers of FIG. 1;

FIG. 3 is a schematic diagram illustrating the details of either one of the ballistics function generators of FIG. 1;

FIG. 4 is a graph illustrating the waveform of the signal segments generated by the ballistics function generator of FIG. 3 relative to a smoothwaveform of the ballistics function.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT Referring now to an embodiment in more detail, reference is made to FIG. 1 wherein range information R is fed to a circuit which is mechanized to generate a superelevation signal 6,, a time of flight signal 1,, a ballistic drift signal n and a crosswind coefficient K in accordance with ballistic equations.

Generally, the range input R is an analog or a digital signal which is produced in any one of several possible ways. For example, the range signal R could be produced by a laser range finder (not shown), in which the pulse count between a transmitted signal and a reflected or returned signal is converted to an analog signal proportional to range. Other techniques might be to use an optical range finder to determine range, or to make an estimate of the range and to set the range value manually.

Once the range is known, the ballistic characteristics of the projectile and environmental conditions must be known in order to generate fire control signals in accordance with the ballistic equations. For example, it is necessary to know the effects of ballistic conditions, such as the projectiles mass, initial velocity, shape, size, spin velocity, and environmental conditions, such as the air density, air temperature, air pressure, crosswind, etc.

Since many of the ballistic characteristics will vary with different projectiles, or ammunitions, the resulting signals such as superelevation s time of flight t,, ballistic drift n and crosswind coefficient K will also vary for each projectile.

It has been discovered that the nonlinear equations of ballistic flight from which superelevation s and time of flight z, are derived, can be produced for projectiles by: a f rst circuit 20 which multiplies or operates on the range information R by an individual ballistic term including an individual normalizing transfer function /R,, for each individual projectile to produce a normalized range signal R/R,,; second circuits 22 and 24 in two parallel channels which operate on the normalized range signal with a single predetermined transfer function common to the ballistics of a plurality of projectile types for generating the nonlinear function signals j R/R,,)and f, (R/R,,) which are related to the selected projectill arid their circuits 26 and 28 for multiplying or operating upon the nonlinear function signals by individual second ballistic terms orunnormalizing transfer functions 6,, and I, which are related to the selected individual projectile. It should be stated that the ballistic terms R 6,, and t, can be considered constants or linear for any fixed set of conditions.

For example, the approximated equation for superelevation s which is the angle by which the projector (such as a gun) is pointed above the line of sight to a target, is:

"=mv; (*rT m 1) 2RK/m 1 and the approximated equation for time of flight I, of the projectile is:

= l ,rtK m where K D drag coefficient R range K pdK p air density d projectile diameter m projectile mass V, projectile initial velocity Ballistic drift 1;, is proportional to superelevation s according to the following equation:

"HF- a n where K,, is a tenn, dependent upon projectile inertia, spin velocity, and lift and moment coefficients, which may be determined for each ammunition. The crosswind coefficient K is found by K =AK,,t, (3b) where K, is an empirically derived coefficient for each ammunition.

As previously stated, it has been determined that signals which are a function of the ballistics equations can be produced by circuits which operate on the range information R in accordance with transfer functions for ballistic terms and normalized functions.

For example, superelevation e, is produced by a circuit which operates on a range signal R in accordance with the following approximate equation:

From these equations, it can be seen that, in implementing the circuits, transfer functions R,,, e and 1,, are ballistic terms which are related to the particular projectile or ammunition ballistic and environmental conditions, and can be treated as linear, for any fixed set of conditions, while the transfer functions f (R/R,,) and f,(R/R,,) are functions which are independent of the projectile type and condition or, in other words, which are common to all of the projectile types. The advantage of this discovery is that only one such nonlinear function generator per ballistic signal need be mechanized for a plurality of projectile types.

Referring now to the block diagram of FIG. l in more detail, the range signal R is first normalized by multiplying by the imalizing term or individual transfer functions related to a selected individual one of plurality of ammunition types l/R, ng a ballistics constant multiplier circuit 20, which is hereinafter referred to as ballistic term multiplier, also, and which is adjustable for each ammunition. The nonnalized range signal R/R, is then fed to function generators 22 and 24 which are connected in parallel circuit relationship to produce nonlinear ballistic function output signals flit/It and f,(R/R,m), respectively in accordance with the single predetermined transfer functions. These nonlinear function output signals are then respectively fed to ballistic constant multipliers 26 and 28 which are hereinafter also referred to a ballistic term multiplier, and which multiply them by the unnormalizing ballistic terms on individual transfer functions 6,, and 1", respectively for the selected projectile type. Consequently, the output signal of the ballistic constant multiplier 26 is related to the superelevation e, for the particular projectile at that particular R in accordance with the preceding ballistic equation (Equation 4). The output of the ballistic constant multiplier 26 is related to the time of flight l; of the selected projectile at the particular range R in accordance with the preceding equation for time of flight Equation 7).

Referring now to the circuit of FIG. 1 in more detail, the range signal R is fed to the ballistic constant multiplier 20, illustrated in FIG. 2 for producing the normalized range signal R/R, in accordance with a normalizing transfer function HR for a selected one of a plurality of projectiles. More specifically, the ballistic constant multiplier 20 is an operational amplifier having a plurality of n parallel selectable gain set input resistance circuit branches which each include one of a plurality of junction FET transistors 34 through 34n connected in series with one of a plurality of resistors 38 through 38n respectively, the resistance circui branches being connected to one input of an amplifier. The subscript n represents the circuit elements in the nth resistance circuit and is equal to a corresponding number of projectilesl In operation, only one of the junction FET transistors 34 thiough 34n is turned on by a positive voltage signal +V applied to its gate terminal through a resistor 36 through 36", respecti ely, while all other ones of the FETs 34 through 34 n are turnild off by a negative voltage -V applied to the gate terminals ereof through the respective resistors 36 through 36n.

Assume, then, that the projectile or ammunition selected has a linear ballistic term or normalizing transfer function 1 /R,,, which is set into the ballistic term multiplier 20 as a normalizing transfer function by the sum of the series resistances in the circuit branch between the source terminal and drain terminal of PET transistor 34 when it is turned on, and the resistor 38 connected between the FET transistor 34 and one input of an operational amplifier 40. In operation a switch 42 is positioned so that a +V voltage is applied through the resistor 36 to the gate terminal of PET transistor 34 to turn it on while all other FET transistors will have a -V voltage applied to their gate terminals and are turned off. The operational amplifier 40 can be a Fairchild 1.1.A709 High Performance Operational Amplifier, manufactured by Fairchild Semiconductor Corporation and described and illustrated in their handbook, "Fairchild Semiconductor Linear integrated Circuits Applications Handbook," 1967.

The operational amplifier 40 is compensated for a gain of unity and a feedback resistor 44 is connected between the output terminal of the operational amplifier and one input terminal thereof so that the gain of the ballistic constant multiplier 20 is proportional to the ratio of the resistance of feedback resistor 44 and the sum of the resistances between the source terminal and drain terminal of the turned on FET transistor 34 and resistor 38 and can be expressed by the term l/R,,. Thus, received range signal R is multiplied by the ballistic term transfer function l/R whereupon the output signal of the ballistic term multiplier 20 is equal to R/R, for the selected ammunition.

Any gain resulting from the resistance circuits associated with turned off FET transistors can be disregarded since the resistance between the source and the drain terminal is very high relative to other circuit resistances. The zero offset of operational amplifier 40 can be set by a center pickoff on a potentiometer 46 wherein the pickoff voltage is substantially 0 volts and is applied to one input terminal of the operational amplifier 40 through a resistor network.

For other projectiles, the ballistic tenn or transfer function l/R, will be different since the resistance of resistors 38 through 38:: is selected to fit the different ballistic terms for different projectiles. Thus, the selected normalized range output signal R/R, is specifically related to the selected projectile. The output signal R/R, is then fed to the ballistic function generator 22 and the ballistic function generator 24.

The ballistic function generator 22 illustrated in detail in FIG. 3 includes a break point selector 50 and a switched resistor network 52, including a plurality of resistance branches which are selectively summed in response to output signals received from the break point selector 50 wherein the selectively summed resistances are coupled to the input of an operational amplifier 54 to vary its gain approximately in accordance with the single nonlinear exponential transfer function of Equation 4 which is common to a plurality of ammunition types.

The break point selector 50 includes a plurality of parallel voltage comparators 56, 58 and 60, which are coupled to receive the normalized range signal R/R, and are set to produce output signals A, B, and C respectively, at three different voltage levels V V, and V,. More specifically, the voltage comparators 56, 58 and 60 are coupled to receive the normalized range voltage R/R, at one input terminal thereof through input resistors 62, 64 and 66, respectively. When a first voltage level V is exceeded by the normalized range voltage R/R, the output of voltage comparator 56, which can be a Fairchild p.A709 High Performance Operational Amplifier, manufactured by Fairchild Semiconductor Corporation and described and illustrated in their handbook, Fairchild Semiconductor Linear Integrated Circuits Applications Handbook, 1967, goes low. The output of voltage comparator 56 is fed to the base terminal of a PNP transistor 68 through a resistor 70 to turn on the transistor 68 and cause the voltage drop across the collector resistor 72 to increase, whereupon the break point select signal A becomes more positive.

The break point select signal B subsequently produced by turning on transistor 74 also becomes more positive when the voltage level V is exceeded by the normalized range input signal R/R, fed to the comparator 58.

In addition, the break point selector voltage C subsequently produced by turning on transistor 76 becomes more positive when the voltage level V is exceeded by the normalized range input signal R/R, received by the comparator 60.

These break point select signals A, B and C are fed to the resistor network 52 to selectively vary the gain of the operational amplifier 54.

The resistor network 52 includes a first set of parallel resistance branches 80 which are coupled to receive the normalized range signal R/R, and are responsive to the break point selector signals A, B and C for setting the gain slope of the function f; (R/R,,) produced at the output of operational amplifier 54. The resistor network 52 also includes a second set of parallel resistance branches 82 which are connected in common to a terminal at a fixed voltage V and are responsive to the break point selector signals A, B and C to bias the projected gain slope level to intercept the coordinants of the nonlinear function (R/R,,) at select points.

More specifically, when the normalized range signal R/R, is less than the first break point voltage level V only a slope set resistor 84 and an intercept set resistor 86 are connected to the input of operational amplifier 54 since no break point select signals A, B, C are received to turn on the junction FET transistors contained in the first set of parallel resistance branches 80 and the second set of parallel resistance branches 82.

The operational amplifier 54 includes an amplifier 87 such as the previously referenced pA709 and has a feedback resistor 8 connected between its output terminal and an input terminal thereof. In addition, a zero offset voltage is applied to another input terminal in the manner previously described. Under these conditions, the combination of the slope set resistor 84 and the intercept resistor 86 operate as gain set resistances wherein the gain of the operational amplifier is proportional to the ratio of the resistance of the feedback resistor 88 and the sum of the parallel resistances of the slope set resistor 84 operating on the normalized range signal R/R, and the intercept set resistor 86 operating on the reference voltage v,,.

Under these conditions, the function generator 22 will generate the first line segment illustrated in FIG. 4 until a voltage V is exceeded by the normalized range signal R/R... It should be noted that this line segment generated by the ballistic function generators and all other subsequent line segments are approximated to the rounded smooth curve for the nonlinear function f; (R/R,,) to within a maximum difference A at any point. These break points and the segment line slope can be selected or chosen empirically by trial and error on a table of values, or by a graphical plot of the function, or mathematically via any of the commonly used techniques for minimizing errors such as least squares curve fit techniques, for example.

Once the value of the normalized range signal R/R, exceeds the first break point voltage V the first break point select signal A is produced by the break point selector circuit 50 and is fed through the resistors 94 and 96 to the gate terminals of PET transistors 90 and 92 in the first set of parallel resistors and the second set of parallel resistors 82, respectively, to turn them on. The sum of the parallel resistances of resistor 84 and the resistance branch, including the resistance between the source terminal and the drain terminal of turned on FET transistor and resistor 98 will effectively reduce the gain slope resistance of the operational amplifier 54, thereby effectively increasing the slope of the second line segment between voltage levels V, and V illustrated in FIG. 4. In addition, for the intercept set bias, the sum of the parallel resistances of resistor 86 and the resistance branch including the resistance between the source terminal and drain' terminal of turned on FET transistor 92 and resistor 100 operate on the voltage +V,, to bias, the operational amplifier gain 54, so that a projection of the second sloping line segment will intercept the coordinate of the graph in FIG. 4 at a predetermined point.

Similarly, the third sloping line segment between break point voltages V and V is produced when the break point select signal B is received at the gate terminals and turns on the FET transistor 102 and 104 so that their source to drain resistance and the resistance of resistors 106 and 108, respectively, are summed in parallel with the previously described resistance branches to increase the gain slope of the third line segment and to further bias the gain slope line segment to another coordinate intercept point.

The fourth line segment following the voltage V;, is produced when the break point select signal C is received at the gates terminal of FET transistors 110 and 112 to turn them on. The resistance branch, including the resistance between the source terminal and drain terminal of turned on FET transistors 110 and 112 and the resistors 114 and 116 are added in parallel to the previously described resistances to further increase the gain. slope of the operational amplifier 54 and to further bias the operational amplifier so that the gain slope line segment, if so projected, would intercept the com dinate at a new intercept set point.

It should, of course, be understood that although a function generator which is capable of generating four line segments has been described, it is possible to increase the accuracy of the curve approximation of this function generator by adding additional comparators and additional resistance circuit branches including FET transistors and resistors so that additional line segments could be generated at additional break points to more closely approximate the smooth curve of FIG.

The resulting output signal on the output terminal of opera; tional amplifier 54 is approximately the nonlinear function f, RE This signal is then fed to the adjustable ballistic terrnmultiplier 26 (FIG. 1) wherein it is multiplied by the ballistics constant or linear unnormalizing transfer function e,,. Structurally, the adjustable ballistics constant multiplier 26 is at; ranged the same as the adjustable ballistics constant multiplier of FIG. 2 with the exception that the value of the resistances 3838n and feedback resistor 44 are selected in accordance with the ballistics constant unnormalizing transfer function e,,

for each ammunition type. The output signal from this adjustable ballistics constant multiplier 26 is proportional to superelevation s in accordance with Equation 4.

The ballistics function generator 24 for generating the nonlinear ballistic function signal f, and the adjustable ballistic constant multiplier 28 for multiplying the nonlinear function signal by the ballistic term linear unnormalizing transfer function 1,, illustrated in FIG. 1 are embodied in the same way as the ballistic function generator 22 of H6. 3 and the adjustable ballistic constant multiplier 26 of H6. 2, respectively, with the exception that the resistances of the resistors therein are selected so that the resultant ballistic function signal output I; will closely approximate the smooth curve and expression represented by Equations 7 and 8.

As previously stated, ballistics drift 1 can be produced by multiplying the superelevation signal 6,, by a ballistic drift term, l(,, at a ballistic term multiplier 27. This ballistic drift term is a function of projectile inertia and spin properties, lift and moment coefficients, and of the projectile mass, size, and drag coefficient. The ballistic term multiplier 27 is similar in construction to the ballistic term multiplier described in FIG. 2.

Also, as previously stated, the crosswind coefficient K may be produced by multiplying the time of flight signal t, by an empirically derived ballistics term K, in a ballistic term multiplier 29. The embodiment of the ballistic term multiplier 29 is similar to the ballistic term multiplier 20 of FIG. 2.

Although the above-described embodiment is directed toward DC operation, it is possible to construct an AC embodiment using the junction FET transistors in a similar circuit arrangement. Furthermore, it is possible to embody the invention by digital techniques and by electromechanical techniques.

While the salient features have been illustrated and described with respect to a particular embodiment, it should be readily apparent that modifications can be made within the spirit and scope of the invention, and it is therefore not desired to limit the invention to the exact details shown and described.

What we claim is:

1. In a device including at least one channel for producing at least one ballistic signal corresponding to range times at least one ballistic equation for the ballistics of a projectile type, the ballistic equation including terms for the effects. of ballistic conditions and the effects of environmental conditions comprising:

first means coupled to receive a range signal for operating on the received range signal by a factor comprising a normalizing transfer function to produce a normalized range signal for a specific projectile type which normalized range signal is standardized relative to a single predetermined transfer function common to the ballistics of a plurality of projectile types;

second means coupled to receive the normalized range signal for operating on the normalized range signal by the single predetermined transfer function common to the ballistics of a plurality of projectile types for generating a nonlinear function signal; and

third means coupled to receive the nonlinear function signal from said second means for operating on the nonlinear function signal by a factor comprising an unnormalizing transfer function for producing the at least one ballistic signal for the selected projectile type.

2. The device of claim 1 in which said first means and said third means operates on the received signals by the transfer functions that include ballistic condition and environmental condition effects on the ballistics ofa specific projectile type.

3. The device of claim 1 in which said second means operates on the received normalized range signal by a predetermined nonlinear transfer function that is common to the ballistics of a plurality of projectile types.

The device of claim 1 in which said second means operates on the received normalized range signals by a predetermined exponential transfer fiinction.

5. The device of claim 1 in which said second means operates on the received normalized range signal by a predetermined transfer function including an exponential function of the base e with an exponent thereof comprising the normalized range signal.

6. The device of claim 1 in which said first means and said third means operate on the received signals by linear factors including terms corresponding to the effects of ballistic conditions and environmental conditions including the projectile mass m, projectile diameter d, drag coefficient K,,, atmospheric density p, and initial projectile velocity V,,.

7. The device of claim 6 in which said third means operates on the received nonlinear function signal by a factor further including the effect of gravity 3 and initial projectile velocity V 8. The device of claim 7 in which said first means operates on the received range signal by approximately the normalizing transfer function /p n and said third means operates on the received nonlinear function signal by approximately the unnormalizing transfer function 9. The device of claim 6 in which said first means operates on the received range signals by approximately the normalizing transfer function /p u and said third means operates on the received nonlinear function signal by approximately the unnormalizing transfer function 10. The device of claim 1 in which said first means and said third means are each adjustable for selectively operating on the received signals by a factor comprising a selected individual one of a plurality of linear. transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.

11. The device of claim 3 in which said first means and said third means are adjustable for selectively operating on the receive signals by selected individual ones of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.

12. The device of claim 8 in which said first means and said third means are adjustable for selectively operating on the received signals by individual ones of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.

13. The device of claim 9 in which said first means and said third means are adjustable for selectively operating on the received signals by selected individual ones of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.

14. The device of claim 1 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating NR/R 1 2( R/R?) 1 where R is the range e equals about 2-7183 l/R is a normalizing constant pd K D for producing the nonlinear function signal.

16. The device of claim 8 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating R is the range e equals about 2-7183 1 1s a. normalizing constant R m for producing the nonlinear function signal.

17. The device of claim 1 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating lRIR L..1 where:

R is the range e equals about 27183 R is a normalizing constant pd K m projectile mass p air density d projectile diameter X drag coefficient for producing the nonlinear function signal.

18. The device of claim 6 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating (RIR l where:

R is the range q q a ab t 2; .1%

is a. normalizing constant z for producing the nonlinear function signal.

19. The device of claim 9 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating R is the range e equals about 12-7183 1 15 {L normalizing constant 2 s n Ill for producing the nonlinear function signal.

20. The device of claim 1 having a first channel and a second channel, said first means being common to both the channels, the channels each including an individual said second means and an individual said third means, said third means included in the first channel being operable to produce a first ballistic signal related to superelevation and said third means included in the second channel being operable to produce a second ballistic signal related to time of flight.

21. The device of claim 2 having a first channel and a second channel, said first means being common to both the channels, the channels each including an individual said second means and an individual said third means, said third means included in the first channel being operable to produce a first ballistic signal and said third means included in the second channel being operable to produce a second ballistic signal.

22. The device of claim 21 in which said third means included in the first channel is operable to produce the first ballistic signal related to superelevation and said third means included in the second channel is operable to produce the second ballistic signal related to time of flight.

23. The device of claim 20 in which said first means operates on the received range signal by approximately the normalizing transfer function said third means included in the first channel operates on the received nonlinear function signal by approximately the unnormalizing transfer function and said third means included in the second channel operates on the received nonlinear function signal by approximately the unnormalizing transfer function n D where:

m projectile mass p= air density d projectile diameter K,, projectile drag coefficient V projectile initial velocity g== gravitational effects.

24. The device of claim 23 in which said second means included in the first channel operates on the received normalized range signal by the single predetermined transfer function approximating Y em/Rn) 1 1 1 =normal1z1ng function 25. The device of claim 23 in which said first means and said third means are adjustable for selectively operating on the received signals by individual transfer functions of a plurality of transfer functions each derived from the effects of ballistic conditions m, d, K and V,,, and environmental conditions p and g on the ballistics of a selected individual one of a plurality of projectile types.

26. The device of claim 24 in which said first means and said third means are adjustable for selectively operating on the received signals by individual transfer functions of a plurality of transfer functions each derived from the effects of ballistic conditions m, d, K and V and environmental conditions p and g on the ballistics of a selected individual one of a plurality of projectile types.

27. In a ballistic computer, the improvement comprising:

a first multiplier circuit having an operational amplifier with a feedback resistor connected between the output terminal thereof and an input terminal thereto, a plurality of parallel resistance branches each having a junction FET transistor connected in series with a resistor, each of said resistance branches being coupled to receive a range signal at one end, and being connected to said input terminal of said operational amplifier at the other end, switch means for applying an electrical signal to gate terminals of said junction FET transistors to turn on one of said junction FET transistors and to turn off the other ones of said junction FET transistors for setting the gain of said operational amplifier to normalize the range signal in accordance with ballistics conditions and environmental conditions for producing a normalized range signal;

a function generator including an operational amplifier having a feedback resistor connected between an output terminal thereof and an input terminal thereto, a break point selector circuit having a plurality of voltage comparators each responsive to individual spaced-apart voltage points and being coupled to receive the normalized range signal for generating a break point signal for each voltage point that the normalized range signal exceeds, a first plurality of resistance branches and a second plurality of resistance branches wherein all of said resistance branches include a resistor and all except one of said resistance branches includes a junction FET transistor connected in series with said resistor, all of said branches being connected at one end to an input of said operational amplifier, the said first plurality of resistance branches being coupled at the other end to receive the normalized range signal for setting the gain slope of the operational amplifier to match a portion of a ballistic function related to a plurality of ammunition, and said second plurality of resistance branches being coupled at the other end to receive a voltage signal to bias the gain slope of said operational amplifier to a predetermined portion of the ballistic function, and said junction FET transistors being responsive to be turned on by individuals of the ones of the break point signals from said comparators to set the gain slope of said operational amplifier by selected ones of said first plurality of resistance branches and to bias the gain slope of said operational amplifier to a predetermined level by selected ones of said second plurality of resistance branches for generating a normalized function signal; and

a second multiplier circuit having an operational amplifier with a feedback resistor connected between the output terminal thereof and an input terminal thereto, a plurality of parallel resistance branches each having a junction F ET transistor connected in series with a resistor, each of said resistance branches being coupled to receive the function signal at one end, and being connected to said input terminal of said operational amplifier at the other end, switch means for applying an electrical signal to gate terminals of said junction FET transistors to turn on one of said junction FET transistors and to turn off the other ones of said junction FET transistors for setting the gain of said operational amplifier to unnormalize the function signal in accordance with ballistic conditions and environmental conditions to produce ballistic signals for selected ammunitions. 

1. In a device including at least one channel for producing at least one ballistic signal corresponding to range times at least one ballistic equation for the ballistics of a projectile type, the ballistic equation including terms for the effects of ballistic conditions and the effects of environmental conditions comprising: first means coupled to receive a range signal for operating on the received range signal by a factor comprising a normalizing transfer function to produce a normalized range signal for a specific projectile type which normalized range signal is standardized relative to a single predetermined transfer function common to the ballistics of a plurality of projectile types; second means coupled to receive the normalized range signal for operating on the normalized range signal by the single predetermined transfer function common to the ballistics of a plurality of projectile types for generating a nonlinear function signal; and third means coupled to receive the nonlinear function signal from said second means for operating on the nonlinear function signal by a factor comprising an unnormalizing transfer function for producing the at least one ballistic signal for the selected projectile type.
 2. The device of claim 1 in which said first means and said third means operates on the received signals by the transfer functions that include ballistic condition and environmental condition effects on the ballistics of a specific projectile type.
 3. The device of claim 1 in which said second means operates on the received normalized range signal by a predetermined nonlinear transfer function that is common to the ballistics of a plurality of projectile types.
 4. The device of claim 1 in which said second means operates on the received normalized range signals by a predetermined exponential transfer function.
 5. The device of claim 1 in which said second means operates on the received normalized range signal by a predetermined transfer function including an exponential function of the base e with an exponent thereof comprising the normalized range signal.
 6. The device of claim 1 in which said first means and said third means operate on the received signals by linear factors including terms corrEsponding to the effects of ballistic conditions and environmental conditions including the projectile mass m, projectile diameter d, drag coefficient KD, atmospheric density p, and initial projectile velocity Vo.
 7. The device of claim 6 in which said third means operates on the received nonlinear function signal by a factor further including the effect of gravity g and initial projectile velocity Vo.
 8. The device of claim 7 in which said first means operates on the received range signal by approximately the normalizing transfer function m/pd2KD and said third means operates on the received nonlinear function signal by approximately the unnormalizing transfer function mg/2pd2VoKD.
 9. The device of claim 6 in which said first means operates on the received range signals by approximately the normalizing transfer function m/pd2KD and said third means operates on the received nonlinear function signal by approximately the unnormalizing transfer function m/pd2VoKD.
 10. The device of claim 1 in which said first means and said third means are each adjustable for selectively operating on the received signals by a factor comprising a selected individual one of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.
 11. The device of claim 3 in which said first means and said third means are adjustable for selectively operating on the receive signals by selected individual ones of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.
 12. The device of claim 8 in which said first means and said third means are adjustable for selectively operating on the received signals by individual ones of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.
 13. The device of claim 9 in which said first means and said third means are adjustable for selectively operating on the received signals by selected individual ones of a plurality of linear transfer functions, each including individual terms derived from the effects of ballistic conditions and environmental conditions on the ballistics of a selected individual one of a plurality of projectile types.
 14. The device of claim 1 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating where R is the range e equals about 2 7183 1/Rn is a normalizing constant m projectile mass p air density d projectile diameter KD drag coefficient for producing the nonlinear function signal.
 15. The device of claim 6 in which said second means operates on the normalized range signal by the predetermined transfer function approximating where: R is the range E equals about 7183 1/Rn is a normalizing constant for producing the nonlinear function signal.
 16. The device of claim 8 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating where R is the range e equals about 2 7183 1/Rn is a normaLizing constant for producing the nonlinear function signal.
 17. The device of claim 1 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating e(R/Rn)-1 where: R is the range e equals about 2 7183 1/Rn is a normalizing constant m projectile mass p air density d projectile diameter KD drag coefficient for producing the nonlinear function signal.
 18. The device of claim 6 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating e(R/Rn)-1 where: R is the range e equals about 2 7183 1/Rn is a normalizing constant for producing the nonlinear function signal.
 19. The device of claim 9 in which said second means operates on the received normalized range signal by the predetermined transfer function approximating e(R/Rn)-1 where: R is the range e equals about 2 7183 1/Rn is a normalizing constant for producing the nonlinear function signal.
 20. The device of claim 1 having a first channel and a second channel, said first means being common to both the channels, the channels each including an individual said second means and an individual said third means, said third means included in the first channel being operable to produce a first ballistic signal related to superelevation and said third means included in the second channel being operable to produce a second ballistic signal related to time of flight.
 21. The device of claim 2 having a first channel and a second channel, said first means being common to both the channels, the channels each including an individual said second means and an individual said third means, said third means included in the first channel being operable to produce a first ballistic signal and said third means included in the second channel being operable to produce a second ballistic signal.
 22. The device of claim 21 in which said third means included in the first channel is operable to produce the first ballistic signal related to superelevation and said third means included in the second channel is operable to produce the second ballistic signal related to time of flight.
 23. The device of claim 20 in which said first means operates on the received range signal by approximately the normalizing transfer function m/pd2KD; said third means included in the first channel operates on the received nonlinear function signal by approximately the unnormalizing transfer function mg/2pd2VoKD; and said third means included in the second channel operates on the received nonlinear function signal by approximately the unnormalizing transfer function m/pd2VoKD where: m projectile mass p air density d projectile diameter KD projectile drag coefficient V0 projectile initial velocity g gravitational effects.
 24. The device of claim 23 in which said second means included in the first channel operates on the received normalized range signal by the single predetermined transfer function approximating and said second means included in the first channel operates on the received normalized range signal by the single predetermined transfer function approximating e(R/Rn)-1 where: R range 1/Rn normalizing function
 25. The device of claim 23 in which said first means and said third means are adjustable for selectively operating on the received signals by individual transfer functions of a plurality of transfer functions each derived from the effects of ballistic conditions m, d, KD and Vo, and environmental conditions p and g on the ballistics of a selected individual one of a plurality of projectile types.
 26. The device of claim 24 in which said first means and said third means are adjustable for selectively operating on the received signals by individual transfer functions of a plurality of transfer functions each derived from the effects of ballistic conditions m, d, KD and Vo and environmental conditions p and g on the ballistics of a selected individual one of a plurality of projectile types.
 27. In a ballistic computer, the improvement comprising: a first multiplier circuit having an operational amplifier with a feedback resistor connected between the output terminal thereof and an input terminal thereto, a plurality of parallel resistance branches each having a junction FET transistor connected in series with a resistor, each of said resistance branches being coupled to receive a range signal at one end, and being connected to said input terminal of said operational amplifier at the other end, switch means for applying an electrical signal to gate terminals of said junction FET transistors to turn on one of said junction FET transistors and to turn off the other ones of said junction FET transistors for setting the gain of said operational amplifier to normalize the range signal in accordance with ballistics conditions and environmental conditions for producing a normalized range signal; a function generator including an operational amplifier having a feedback resistor connected between an output terminal thereof and an input terminal thereto, a break point selector circuit having a plurality of voltage comparators each responsive to individual spaced-apart voltage points and being coupled to receive the normalized range signal for generating a break point signal for each voltage point that the normalized range signal exceeds, a first plurality of resistance branches and a second plurality of resistance branches wherein all of said resistance branches include a resistor and all except one of said resistance branches includes a junction FET transistor connected in series with said resistor, all of said branches being connected at one end to an input of said operational amplifier, the said first plurality of resistance branches being coupled at the other end to receive the normalized range signal for setting the gain slope of the operational amplifier to match a portion of a ballistic function related to a plurality of ammunition, and said second plurality of resistance branches being coupled at the other end to receive a voltage signal to bias the gain slope of said operational amplifier to a predetermined portion of the ballistic function, and said junction FET transistors being responsive to be turned on by individuals of the ones of the break point signals from said comparators to set the gain slope of said operational amplifier by selected ones of said first plurality of resistance branches and to bias the gain slope of said operational amplifier to a predetermined level by selected ones of said second plurality of resistance branches for generating a normalized function signal; and a second multiplier circuit having an operational amplifier with a feedback resistor connected between the output terminal thereof and an input terminal thereto, a plurality of parallel resistance branches each having a junction FET transistor connected in series with a resistor, each of said resistance branches being coupled to receive the function signal at one end, and being connected to said input terminal of said operational amplifier at The other end, switch means for applying an electrical signal to gate terminals of said junction FET transistors to turn on one of said junction FET transistors and to turn off the other ones of said junction FET transistors for setting the gain of said operational amplifier to unnormalize the function signal in accordance with ballistic conditions and environmental conditions to produce ballistic signals for selected ammunitions. 